Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C13 ⋊ #2232 |
150 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|c^2=d,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,e^c=ef,f^c=fg,h^c=h^12161 conjugacy classes — view the full character table.
| maximal subgroup of | #15776120, #15776121, #15776131, … |
| maximal normal subgroup of | #15776120, #15776121, #15776131, … |
| maximal quotient of | #15779205, #15779417, #15779858, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6688);